Affiliation:
1. Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain
Abstract
An explicit difference method is considered for solving fractional diffusion and fractional diffusion-wave equations where the time derivative is a fractional derivative in the Caputo form. For the fractional diffusion equation, the L1 discretization formula of the fractional derivative is employed, whereas the L2 discretization formula is used for the fractional diffusion-wave equation. In both equations, the spatial derivative is approximated by means of the three-point centered formula. The accuracy of the present method is similar to other well-known explicit difference schemes, but its region of stability is larger. The stability analysis is carried out by means of a kind of fractional von Neumann (or Fourier) method. The stability bound so obtained, which is given in terms of the Riemann zeta function, is checked numerically.
Subject
Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,Applied Mathematics,Mechanical Engineering,Control and Systems Engineering
Cited by
69 articles.
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